Given this linear programming model, solve the model and then answer the questions that follow.

Maximize$12$x$1+18$x$2+15$x$3$where x$1=$ the quantity of product $1$ to make etc.Subject to$$

Machine$5$x$1+4$x$2+3$x$3160$minutesLabor$4$x$1+10$x$2+4$x$3288$hoursMaterials$2$x$1+2$x$2+4$x$3200$poundsProduct $2$x$216$units$$x$1,$ x$2,$ x$30$

a$-1.$ Are any constraints binding?

multiple choice $1$

Yes

No

a$-2.$ If so$,$ which one$($s$)?$

multiple choice $2$

Machine and materials

Machine and labor

Materials

Labor

None

b$-1.$ If the profit on product $3$ changed to $$22$ a unit, would the decision variables'values change?

multiple choice $3$

Yes

No

b$-2.$ What would the new value of the objective function be$?$

c$-1.$ If the profit on product $1$ changed to $$22$ a unit, would the decision variables'values change?

multiple choice $4$

Yes

No

c$-2.$ Will the objective function value change, based on the change in c$-1?$

multiple choice $5$

Yes

No

d$-1.$ If $10$ hours less of labor time were available, would the decision variables values change?

multiple choice $6$

Yes

No

d$-2.$ Will the objective function value change, based on the change in d$-1?$

multiple choice $7$

Yes

No

e$.$ If the manager decided that as many as $20$ units of product $2$ could be produced $($instead of $16),$ how much additional profit would be generated?

multiple choice $8$

$$0$

$$4$

$$16$

$$72$

f$-1.$ If profit per unit on each product increased by $$1,$ would the optimal values of the decision variables change?

multiple choice $9$

Yes

No

f$-2.$ What would be the new value of the objective function?